Abstract
Cardiovascular disease is a major threat to human health. The study on the pathogenesis and prevention of cardiovascular disease has received special attention. In this paper, we have contributed to the derivation of a mathematical model for the nonlinear waves in an artery. From the Navier–Stokes equations and continuity equation, the vorticity equation satisfied by the blood flow is established. And based on the multiscale analysis and perturbation method, a new model of the Boussinesq equation with viscous term is derived to describe the propagation of a viscous fluid through a thin tube. In order to be more consistent with the flow of the fluid, the time-fractional Boussinesq equation with viscous term is deduced by employing the semi-inverse method and the fractional variational principle. Moreover, the approximate analytical solution of the fractional equation is obtained, and the effect of viscosity on the amplitude and width of the wave is studied. Finally, the effects of the fractional order parameters and vessel radius on blood flow volume are discussed and analyzed.
Highlights
In the field of biological rheology, the rheology which is related to the blood, blood vessels, and heart that constitute the human blood circulation has been developed rapidly
Organism is a completely nonlinear complex medium, and both the blood composition and the structure of blood vessels show obvious nonlinear characteristics. e nonlinearity of blood flow has long been discovered by Womersley [4, 5] and McDonald [6, 7], which provides a new direction and way for people to understand the law of life movement
Choy [14] deduced the mathematical model of nonlinear wave modulation of artery with stenosis
Summary
In the field of biological rheology, the rheology which is related to the blood, blood vessels, and heart that constitute the human blood circulation has been developed rapidly. Fractional derivative theory and methods [15,16,17,18] are widely used in the study of nonequilibrium systems of Complexity various intermediate processes and critical phenomena in physics and mechanics, especially in nonlinear science [19,20,21,22]. E structure of the full article is as follows: in Section 2, the Boussinesq equation with viscous term is derived by the multiscale analysis and perturbation method and used for the first time to describe blood flow. The effects of fractional order, vascular radius, and blood flow velocity on stroke volume are analyzed and studied
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